Millennials, the generation weighed down with student loans that abhors taking on more debt, are embracing a once-derided financial product: Prepaid debit cards.

A third of Americans 18-34 years old have used a reloadable prepaid debit card compared with only a quarter of Americans overall, according to a new survey by TD Bank. And 60 percent of millennials would consider using one compared with half of the overall population.

"These cards are much more mainstream than many people think," said Tami Farrow, TD Bank's head of retail deposit payment products.

One reason: They've cleaned up their act. Prepaid debit cards used to be notorious for charging high fees, including several prepaid cards promoted by celebrities, such as Justin Bieber and Kim Kardashian. But criticism from consumer advocates—and cheaper offerings from American Express and Chase in recent years—put pressure on the bad actors to lower fees or leave the market, McBride said.

A 2014 Pew study found that fees on prepaid debit cards offered by large banks were "economical compared to the cards studied in 2012."

TD Bank found that 21 percent of prepaid debit card users has more than $100,000 in income. Among prepaid debit card users, 46 percent said the cards let them budget and keep track of their spending better. That number rises to 60 percent among millennials.

"One of the benefits that came through loud and clear in the survey is that millennials like the convenience, the simplicity and the predictability of the cards," Farrow said. TD Bank launched its own prepaid debit card in March.

More than half of prepaid debit cards have no monthly fee or will waive the monthly fee if a certain amount is loaded on the card, according to a new Bankrate.com survey. "It's easier to avoid fees altogether on prepaid debit cards," said Greg McBride, Bankrate's chief analyst.

Bankrate found that 48 percent of prepaid debit cards have an activation fee, which ranges from $1.88 to $9.95, depending on where the card is purchased.

That's not to say that some prepaid debit cards don't come with stupid fees. Bankrate found that 16 percent of prepaid debit cards still charge for customer service calls (down from 27 percent in 2014).

"You should always closely review the terms and conditions of any card to find those hidden fees," Hardekopf said.